ionic solids and radius ratio effect

1. Ionic solids

2. Introduction
• Ionic Solids are solids composed of oppositely
charged ions. They consist of positively
charged cations and negatively charged
anions.
• In an ionic compound, the cations and anions
are arranged in space to form an extended 3-D
array that maximizes the number of attractive
electrostatic interactions and minimizes the
number of repulsive electrostatic interactions.

3. •The electrostatic energy of the interaction between two
charged particles is proportional to the product of the charges
on the particles and inversely proportional to the distance
between them:
electrostatic energy ∝ Q1Q2/ r

4. Properties of ionic solids
• Ionic solids are generally high melting (more than
150 degrees C). Ionic solids are hard and brittle. Ionic
solids melt to form liquids that are electrical
conductors because the ions are free to move.
• Ionic solids that are water soluble, dissolve to form
solutions that are electrical conductors.
• Ionic solids are brittle and hard because the
electrostatic attractions in the solid again hold the
ions in definite positions.
• Ionic solids can be composed of simple ions as see in
NaCl (sodium chloride) and like in ammonium nitrate
NH4NO3 with NH4
+ and NO3
- ions.

5. Radius ratio effect and coordination
number
• By using radius ratio rule, it is possible to predict the
cation /anion coordination number in any
compound. So radius ratio is a useful measure in
establishing the structure of ionic solids.
• radius ratio is the ratio of the ionic radius of the
cation to the ionic radius of the anion in a cation-
anion compound.
• Relation between the radius, co-ordination number and
the structural arrangement of the molecule.
• radius ratio =

6. Structural analysis by radius ratio rule
S.NO. RADIUS
RATIO
CO-ORDINATION
NUMBER
SHAPE EXAMPLE
1. 0.0 – 0.155 2 Linear HF-
2. 0.155–0.225 3 Triangular
planar
B
3. 0.225– 0.414 4 Tetrahedral ZnS
4. 0.414– 0.732 6 Octahedral NaCl
5. 0.732 – 1.0 8 Body-centered
cubic
CsCl

7. Example of radius ratio rule
• Consider zinc sulphide in which
Zinc ions thus prefer the tetrahedral holes in the close
packed lattice of sulphide ions.
• In the same way, we can predict that sodium ions will
prefer octahedral holes in a close packed lattice of chloride
ions .
With larger cations, such as cesium, the ratio increases
beyond the limit for a coordination number of 6 (0.414 -
0.732). Cesium ions now occupy cubic sites, i.e.,
coordination number of cations increases to 8 in a lattice of
chloride ions .

8. Calculation of limiting radius ratio
1. Triangular planar
cos30◦= CD/BD

10. 3.Tetrahedral
• AB2 =BD2 +AD2
AB =r+ +r - and AD= r -
In ∆ ACE
AC2 =AE2 +EC2
BD=1/√2 r –
put the value of BD in the main equation and
we get radius ratio =0.225

11. • Limitation of the Radius Ratio Rule
(i) Each ion is considered as a hard sphere for determining the optimum
arrangement of ions in the crystal lattice. This is far form reality and serious errors
can be made if anions get polarized and the bonding the intermediate (partially
covalent) in character.
(ii) Some compounds may crystallize in more than one modification with different
coordination numbers. In such case, anion-anion repulsions and hence internuclear
distance would be different.
(iii) alkali metals halide
• Effective radius of a cation is greatly influenced by the anions with the
consequence that the radius ratio changes. For example, AgF and NaCl crystallize
out in NaCl type of structure with coordination No. 6 and if we assume that the
size of F- remains constant than Ag+ is bigger than Na+. On the other hand, for a
given size for a chloride ion in AgCI and NaCI, the sizes of cations are reversed, that
is, Na+ is bigger than Ag+. It is also true for their bromides. This is understandable
because Ag+ is softer than N+ and introduces relatively more covalent character
with Polarizable anions like CI- and Br-